Safe Haskell	None
Language	Haskell98

Numeric.LAPACK.Matrix.Shape

Synopsis

type General height width = Full Big Big height width
type Tall height width = Full Big Small height width
type Wide height width = Full Small Big height width
type Square size = Full Small Small size size
data Full vert horiz height width = Full {
- fullOrder :: Order
- fullExtent :: Extent vert horiz height width
}
fullHeight :: (C vert, C horiz) => Full vert horiz height width -> height
fullWidth :: (C vert, C horiz) => Full vert horiz height width -> width
data Order
- = RowMajor
- | ColumnMajor
flipOrder :: Order -> Order
general :: Order -> height -> width -> General height width
square :: Order -> sh -> Square sh
wide :: (C height, C width) => Order -> height -> width -> Wide height width
tall :: (C height, C width) => Order -> height -> width -> Tall height width
data Split lower vert horiz height width
type SplitGeneral lower height width = Split lower Big Big height width
data Triangle = Triangle
data Reflector = Reflector
splitGeneral :: lower -> Order -> height -> width -> SplitGeneral lower height width
splitFromFull :: lower -> Full vert horiz height width -> Split lower vert horiz height width
data Hermitian size = Hermitian {
- hermitianOrder :: Order
- hermitianSize :: size
}
hermitian :: Order -> size -> Hermitian size
data Triangular lo diag up size = Triangular {
- triangularDiag :: diag
- triangularUplo :: (lo, up)
- triangularOrder :: Order
- triangularSize :: size
}
type Identity = Triangular Empty Unit Empty
type Diagonal = Triangular Empty NonUnit Empty
type LowerTriangular diag = Triangular Filled diag Empty
type UpperTriangular diag = Triangular Empty diag Filled
type Symmetric = FlexSymmetric NonUnit
diagonal :: Order -> size -> Triangular Empty NonUnit Empty size
lowerTriangular :: Order -> size -> LowerTriangular NonUnit size
upperTriangular :: Order -> size -> UpperTriangular NonUnit size
symmetric :: Order -> size -> Symmetric size
autoDiag :: TriDiag diag => diag
autoUplo :: (Content lo, Content up) => (lo, up)
type DiagUpLo lo up = (DiagUpLoC lo up, DiagUpLoC up lo)
switchDiagUpLoSym :: (Content lo, Content up) => f Empty Empty -> f Empty Filled -> f Filled Empty -> f Filled Filled -> f lo up
class TriDiag diag
switchTriDiag :: TriDiag diag => f Unit -> f NonUnit -> f diag
data Unit = Unit
data NonUnit = NonUnit
data Banded sub super vert horiz height width = Banded {
- bandedOffDiagonals :: (UnaryProxy sub, UnaryProxy super)
- bandedOrder :: Order
- bandedExtent :: Extent vert horiz height width
}
type BandedGeneral sub super = Banded sub super Big Big
type BandedSquare sub super size = Banded sub super Small Small size size
type BandedLowerTriangular sub size = BandedSquare sub U0 size
type BandedUpperTriangular super size = BandedSquare U0 super size
type BandedDiagonal size = BandedSquare U0 U0 size
data BandedIndex row column
- = InsideBox row column
- | VertOutsideBox Int column
- | HorizOutsideBox row Int
bandedGeneral :: (UnaryProxy sub, UnaryProxy super) -> Order -> height -> width -> Banded sub super Big Big height width
bandedSquare :: (UnaryProxy sub, UnaryProxy super) -> Order -> size -> Banded sub super Small Small size size
bandedFromFull :: (UnaryProxy sub, UnaryProxy super) -> Full vert horiz height width -> Banded sub super vert horiz height width
type UnaryProxy a = Proxy (Un a)
addOffDiagonals :: (Natural subA, Natural superA, Natural subB, Natural superB, (subA :+: subB) ~ subC, (superA :+: superB) ~ superC) => (UnaryProxy subA, UnaryProxy superA) -> (UnaryProxy subB, UnaryProxy superB) -> ((Nat subC, Nat superC), (UnaryProxy subC, UnaryProxy superC))
class Content c
data BandedHermitian off size = BandedHermitian {
- bandedHermitianOffDiagonals :: UnaryProxy off
- bandedHermitianOrder :: Order
- bandedHermitianSize :: size
}
bandedHermitian :: UnaryProxy off -> Order -> size -> BandedHermitian off size
class C shape => Box shape
type family HeightOf shape
type family WidthOf shape
height :: Box shape => shape -> HeightOf shape
width :: Box shape => shape -> WidthOf shape

Documentation

type General height width = Full Big Big height width Source #

type Tall height width = Full Big Small height width Source #

type Wide height width = Full Small Big height width Source #

type Square size = Full Small Small size size Source #

data Full vert horiz height width Source #

Constructors

Full
Fields fullOrder :: Order fullExtent :: Extent vert horiz height width

Instances

(C vert, C horiz, C size, size ~ height, Eq height, C width) => Multiply (Hermitian size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Hermitian size) (Full vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (Hermitian size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (Hermitian size) (Full vert horiz height width)) a Source #
(Natural offDiag, C vert, C horiz, C size, size ~ height, Eq height, C width, Eq width) => Multiply (BandedHermitian offDiag size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (BandedHermitian offDiag size) (Full vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (BandedHermitian offDiag size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (BandedHermitian offDiag size) (Full vert horiz height width)) a Source #
(C vert, C horiz, Eq height, Eq width) => Eq (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Full vert horiz height width -> Full vert horiz height width -> Bool # (/=) :: Full vert horiz height width -> Full vert horiz height width -> Bool #
(C vert, C horiz, Show height, Show width) => Show (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Full vert horiz height width -> ShowS # show :: Full vert horiz height width -> String # showList :: [Full vert horiz height width] -> ShowS #
(C vert, C horiz, C height, C width) => C (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods size :: Full vert horiz height width -> Int # uncheckedSize :: Full vert horiz height width -> Int #
(C vert, C horiz, Indexed height, Indexed width) => Indexed (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type Index (Full vert horiz height width) :: Type # Methods indices :: Full vert horiz height width -> [Index (Full vert horiz height width)] # offset :: Full vert horiz height width -> Index (Full vert horiz height width) -> Int # uncheckedOffset :: Full vert horiz height width -> Index (Full vert horiz height width) -> Int # inBounds :: Full vert horiz height width -> Index (Full vert horiz height width) -> Bool # sizeOffset :: Full vert horiz height width -> (Int, Index (Full vert horiz height width) -> Int) # uncheckedSizeOffset :: Full vert horiz height width -> (Int, Index (Full vert horiz height width) -> Int) #
(C vert, C horiz, InvIndexed height, InvIndexed width) => InvIndexed (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods indexFromOffset :: Full vert horiz height width -> Int -> Index (Full vert horiz height width) # uncheckedIndexFromOffset :: Full vert horiz height width -> Int -> Index (Full vert horiz height width) #
(C vert, C horiz, NFData height, NFData width) => NFData (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Full vert horiz height width -> () #
(C vert, C horiz, C height, C width) => Box (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Full vert horiz height width) :: Type Source # type WidthOf (Full vert horiz height width) :: Type Source # Methods height :: Full vert horiz height width -> HeightOf (Full vert horiz height width) Source # width :: Full vert horiz height width -> WidthOf (Full vert horiz height width) Source #
(C vert, C horiz, Indexed height, Indexed width) => Indexed (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Indexed Methods (#!) :: Floating a => Array (Full vert horiz height width) a -> (Index (HeightOf (Full vert horiz height width)), Index (WidthOf (Full vert horiz height width))) -> a Source #
(C vert, C horiz, Eq height, C width, C height) => MultiplyLeft (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (<#) :: Floating a => Vector (HeightOf (Full vert horiz height width)) a -> Array (Full vert horiz height width) a -> Vector (WidthOf (Full vert horiz height width)) a Source #
(C vert, C horiz, Eq width, C width, C height) => MultiplyRight (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (#>) :: Floating a => Array (Full vert horiz height width) a -> Vector (WidthOf (Full vert horiz height width)) a -> Vector (HeightOf (Full vert horiz height width)) a Source #
(vert ~ Small, horiz ~ Small, C width, C height, height ~ width) => Inverse (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods inverse :: Floating a => Array (Full vert horiz height width) a -> Array (Full vert horiz height width) a Source #
(vert ~ Small, horiz ~ Small, C width, C height, height ~ width) => Solve (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods solve :: (Floating a, HeightOf (Full vert horiz height width) ~ height0, Eq height0, C horiz0, C vert0, C nrhs) => Array (Full vert horiz height width) a -> Full0 vert0 horiz0 height0 nrhs a -> Full0 vert0 horiz0 height0 nrhs a Source #
(C vert, C horiz, C height, C width) => FormatArray (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Format Methods formatArray :: Floating a => String -> Array (Full vert horiz height width) a -> Box Source #
(C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vert horiz height width) (Hermitian size) :: Type Methods (<#>) :: Floating a => Array (Full vert horiz height width) a -> Array (Hermitian size) a -> Array (Multiplied (Full vert horiz height width) (Hermitian size)) a Source #
(Natural offDiag, C vert, C horiz, C size, size ~ width, Eq width, C height, Eq height) => Multiply (Full vert horiz height width) (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vert horiz height width) (BandedHermitian offDiag size) :: Type Methods (<#>) :: Floating a => Array (Full vert horiz height width) a -> Array (BandedHermitian offDiag size) a -> Array (Multiplied (Full vert horiz height width) (BandedHermitian offDiag size)) a Source #
(Content lo, Content up, TriDiag diag, C vert, C horiz, C size, size ~ height, Eq height, C width) => Multiply (Triangular lo diag up size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Triangular lo diag up size) (Full vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (Triangular lo diag up size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (Triangular lo diag up size) (Full vert horiz height width)) a Source #
(Content lo, Content up, TriDiag diag, C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vert horiz height width) (Triangular lo diag up size) :: Type Methods (<#>) :: Floating a => Array (Full vert horiz height width) a -> Array (Triangular lo diag up size) a -> Array (Multiplied (Full vert horiz height width) (Triangular lo diag up size)) a Source #
(C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB, C vertA, C horizA, C vertB, C horizB) => Multiply (Full vertA horizA heightA widthA) (Full vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vertA horizA heightA widthA) (Full vertB horizB heightB widthB) :: Type Methods (<#>) :: Floating a => Array (Full vertA horizA heightA widthA) a -> Array (Full vertB horizB heightB widthB) a -> Array (Multiplied (Full vertA horizA heightA widthA) (Full vertB horizB heightB widthB)) a Source #
(Natural sub, Natural super, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB) :: Type Methods (<#>) :: Floating a => Array (Full vertA horizA heightA widthA) a -> Array (Banded sub super vertB horizB heightB widthB) a -> Array (Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB)) a Source #
(Natural sub, Natural super, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB) :: Type Methods (<#>) :: Floating a => Array (Banded sub super vertA horizA heightA widthA) a -> Array (Full vertB horizB heightB widthB) a -> Array (Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB)) a Source #
type Index (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type Index (Full vert horiz height width) = (Index height, Index width)
type HeightOf (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Full vert horiz height width) = height
type WidthOf (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Full vert horiz height width) = width

fullHeight :: (C vert, C horiz) => Full vert horiz height width -> height Source #

fullWidth :: (C vert, C horiz) => Full vert horiz height width -> width Source #

data Order Source #

Constructors

RowMajor
ColumnMajor

Instances

Eq Order Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Order -> Order -> Bool # (/=) :: Order -> Order -> Bool #
Show Order Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Order -> ShowS # show :: Order -> String # showList :: [Order] -> ShowS #
NFData Order Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Order -> () #

flipOrder :: Order -> Order Source #

general :: Order -> height -> width -> General height width Source #

square :: Order -> sh -> Square sh Source #

wide :: (C height, C width) => Order -> height -> width -> Wide height width Source #

tall :: (C height, C width) => Order -> height -> width -> Tall height width Source #

data Split lower vert horiz height width Source #

Instances

(C vert, C horiz, Eq lower, Eq height, Eq width) => Eq (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Split lower vert horiz height width -> Split lower vert horiz height width -> Bool # (/=) :: Split lower vert horiz height width -> Split lower vert horiz height width -> Bool #
(C vert, C horiz, Show lower, Show height, Show width) => Show (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Split lower vert horiz height width -> ShowS # show :: Split lower vert horiz height width -> String # showList :: [Split lower vert horiz height width] -> ShowS #
(Eq lower, C vert, C horiz, C height, C width) => C (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods size :: Split lower vert horiz height width -> Int # uncheckedSize :: Split lower vert horiz height width -> Int #
(Eq lower, C vert, C horiz, Indexed height, Indexed width) => Indexed (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type Index (Split lower vert horiz height width) :: Type # Methods indices :: Split lower vert horiz height width -> [Index (Split lower vert horiz height width)] # offset :: Split lower vert horiz height width -> Index (Split lower vert horiz height width) -> Int # uncheckedOffset :: Split lower vert horiz height width -> Index (Split lower vert horiz height width) -> Int # inBounds :: Split lower vert horiz height width -> Index (Split lower vert horiz height width) -> Bool # sizeOffset :: Split lower vert horiz height width -> (Int, Index (Split lower vert horiz height width) -> Int) # uncheckedSizeOffset :: Split lower vert horiz height width -> (Int, Index (Split lower vert horiz height width) -> Int) #
(Eq lower, C vert, C horiz, InvIndexed height, InvIndexed width) => InvIndexed (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods indexFromOffset :: Split lower vert horiz height width -> Int -> Index (Split lower vert horiz height width) # uncheckedIndexFromOffset :: Split lower vert horiz height width -> Int -> Index (Split lower vert horiz height width) #
(NFData lower, C vert, C horiz, NFData height, NFData width) => NFData (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Split lower vert horiz height width -> () #
(Eq lower, C vert, C horiz, C height, C width) => Box (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Split lower vert horiz height width) :: Type Source # type WidthOf (Split lower vert horiz height width) :: Type Source # Methods height :: Split lower vert horiz height width -> HeightOf (Split lower vert horiz height width) Source # width :: Split lower vert horiz height width -> WidthOf (Split lower vert horiz height width) Source #
(Eq lower, C vert, C horiz, C height, C width) => FormatArray (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Format Methods formatArray :: Floating a => String -> Array (Split lower vert horiz height width) a -> Box Source #
type Index (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type Index (Split lower vert horiz height width) = (Either lower Triangle, (Index height, Index width))
type HeightOf (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Split lower vert horiz height width) = height
type WidthOf (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Split lower vert horiz height width) = width

type SplitGeneral lower height width = Split lower Big Big height width Source #

data Triangle Source #

Constructors

Triangle

Instances

Eq Triangle Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Triangle -> Triangle -> Bool # (/=) :: Triangle -> Triangle -> Bool #
Show Triangle Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Triangle -> ShowS # show :: Triangle -> String # showList :: [Triangle] -> ShowS #
NFData Triangle Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Triangle -> () #

data Reflector Source #

Constructors

Reflector

Instances

Eq Reflector Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Reflector -> Reflector -> Bool # (/=) :: Reflector -> Reflector -> Bool #
Show Reflector Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Reflector -> ShowS # show :: Reflector -> String # showList :: [Reflector] -> ShowS #
NFData Reflector Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Reflector -> () #

splitGeneral :: lower -> Order -> height -> width -> SplitGeneral lower height width Source #

splitFromFull :: lower -> Full vert horiz height width -> Split lower vert horiz height width Source #

data Hermitian size Source #

Store the upper triangular half of a real symmetric or complex Hermitian matrix.

Constructors

Hermitian
Fields hermitianOrder :: Order hermitianSize :: size

Instances

Eq size => Eq (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Hermitian size -> Hermitian size -> Bool # (/=) :: Hermitian size -> Hermitian size -> Bool #
Show size => Show (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Hermitian size -> ShowS # show :: Hermitian size -> String # showList :: [Hermitian size] -> ShowS #
C size => C (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods size :: Hermitian size -> Int # uncheckedSize :: Hermitian size -> Int #
Indexed size => Indexed (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type Index (Hermitian size) :: Type # Methods indices :: Hermitian size -> [Index (Hermitian size)] # offset :: Hermitian size -> Index (Hermitian size) -> Int # uncheckedOffset :: Hermitian size -> Index (Hermitian size) -> Int # inBounds :: Hermitian size -> Index (Hermitian size) -> Bool # sizeOffset :: Hermitian size -> (Int, Index (Hermitian size) -> Int) # uncheckedSizeOffset :: Hermitian size -> (Int, Index (Hermitian size) -> Int) #
InvIndexed size => InvIndexed (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods indexFromOffset :: Hermitian size -> Int -> Index (Hermitian size) # uncheckedIndexFromOffset :: Hermitian size -> Int -> Index (Hermitian size) #
NFData size => NFData (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Hermitian size -> () #
C size => Box (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Hermitian size) :: Type Source # type WidthOf (Hermitian size) :: Type Source # Methods height :: Hermitian size -> HeightOf (Hermitian size) Source # width :: Hermitian size -> WidthOf (Hermitian size) Source #
Indexed size => Indexed (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Indexed Methods (#!) :: Floating a => Array (Hermitian size) a -> (Index (HeightOf (Hermitian size)), Index (WidthOf (Hermitian size))) -> a Source #
(Eq shape, C shape) => MultiplyLeft (Hermitian shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (<#) :: Floating a => Vector (HeightOf (Hermitian shape)) a -> Array (Hermitian shape) a -> Vector (WidthOf (Hermitian shape)) a Source #
(Eq shape, C shape) => MultiplyRight (Hermitian shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (#>) :: Floating a => Array (Hermitian shape) a -> Vector (WidthOf (Hermitian shape)) a -> Vector (HeightOf (Hermitian shape)) a Source #
C shape => Inverse (Hermitian shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods inverse :: Floating a => Array (Hermitian shape) a -> Array (Hermitian shape) a Source #
C shape => Solve (Hermitian shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods solve :: (Floating a, HeightOf (Hermitian shape) ~ height, Eq height, C horiz, C vert, C nrhs) => Array (Hermitian shape) a -> Full vert horiz height nrhs a -> Full vert horiz height nrhs a Source #
C size => FormatArray (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Format Methods formatArray :: Floating a => String -> Array (Hermitian size) a -> Box Source #
(C shapeA, shapeA ~ shapeB, Eq shapeB) => Multiply (Hermitian shapeA) (Hermitian shapeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Hermitian shapeA) (Hermitian shapeB) :: Type Methods (<#>) :: Floating a => Array (Hermitian shapeA) a -> Array (Hermitian shapeB) a -> Array (Multiplied (Hermitian shapeA) (Hermitian shapeB)) a Source #
(C vert, C horiz, C size, size ~ height, Eq height, C width) => Multiply (Hermitian size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Hermitian size) (Full vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (Hermitian size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (Hermitian size) (Full vert horiz height width)) a Source #
(C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vert horiz height width) (Hermitian size) :: Type Methods (<#>) :: Floating a => Array (Full vert horiz height width) a -> Array (Hermitian size) a -> Array (Multiplied (Full vert horiz height width) (Hermitian size)) a Source #
type Index (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type Index (Hermitian size) = (Index size, Index size)
type HeightOf (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Hermitian size) = size
type WidthOf (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Hermitian size) = size

hermitian :: Order -> size -> Hermitian size Source #

data Triangular lo diag up size Source #

Constructors

Triangular
Fields triangularDiag :: diag triangularUplo :: (lo, up) triangularOrder :: Order triangularSize :: size

Instances

(Eq diag, Eq lo, Eq up, Eq size) => Eq (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Triangular lo diag up size -> Triangular lo diag up size -> Bool # (/=) :: Triangular lo diag up size -> Triangular lo diag up size -> Bool #
(Show diag, Show lo, Show up, Show size) => Show (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Triangular lo diag up size -> ShowS # show :: Triangular lo diag up size -> String # showList :: [Triangular lo diag up size] -> ShowS #
(Content lo, TriDiag diag, Content up, C size) => C (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods size :: Triangular lo diag up size -> Int # uncheckedSize :: Triangular lo diag up size -> Int #
(Content lo, TriDiag diag, Content up, Indexed size) => Indexed (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type Index (Triangular lo diag up size) :: Type # Methods indices :: Triangular lo diag up size -> [Index (Triangular lo diag up size)] # offset :: Triangular lo diag up size -> Index (Triangular lo diag up size) -> Int # uncheckedOffset :: Triangular lo diag up size -> Index (Triangular lo diag up size) -> Int # inBounds :: Triangular lo diag up size -> Index (Triangular lo diag up size) -> Bool # sizeOffset :: Triangular lo diag up size -> (Int, Index (Triangular lo diag up size) -> Int) # uncheckedSizeOffset :: Triangular lo diag up size -> (Int, Index (Triangular lo diag up size) -> Int) #
(Content lo, TriDiag diag, Content up, InvIndexed size) => InvIndexed (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods indexFromOffset :: Triangular lo diag up size -> Int -> Index (Triangular lo diag up size) # uncheckedIndexFromOffset :: Triangular lo diag up size -> Int -> Index (Triangular lo diag up size) #
(Content lo, TriDiag diag, Content up, NFData size) => NFData (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Triangular lo diag up size -> () #
(Content lo, TriDiag diag, Content up, C size) => Box (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Triangular lo diag up size) :: Type Source # type WidthOf (Triangular lo diag up size) :: Type Source # Methods height :: Triangular lo diag up size -> HeightOf (Triangular lo diag up size) Source # width :: Triangular lo diag up size -> WidthOf (Triangular lo diag up size) Source #
(Content lo, TriDiag diag, Content up, Indexed size) => Indexed (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Indexed Methods (#!) :: Floating a => Array (Triangular lo diag up size) a -> (Index (HeightOf (Triangular lo diag up size)), Index (WidthOf (Triangular lo diag up size))) -> a Source #
(Content lo, Content up, TriDiag diag, Eq shape, C shape) => MultiplyLeft (Triangular lo diag up shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (<#) :: Floating a => Vector (HeightOf (Triangular lo diag up shape)) a -> Array (Triangular lo diag up shape) a -> Vector (WidthOf (Triangular lo diag up shape)) a Source #
(Content lo, Content up, TriDiag diag, Eq shape, C shape) => MultiplyRight (Triangular lo diag up shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (#>) :: Floating a => Array (Triangular lo diag up shape) a -> Vector (WidthOf (Triangular lo diag up shape)) a -> Vector (HeightOf (Triangular lo diag up shape)) a Source #
(DiagUpLo lo up, TriDiag diag, C shape) => Inverse (Triangular lo diag up shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods inverse :: Floating a => Array (Triangular lo diag up shape) a -> Array (Triangular lo diag up shape) a Source #
(Content lo, Content up, TriDiag diag, C shape) => Solve (Triangular lo diag up shape) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods solve :: (Floating a, HeightOf (Triangular lo diag up shape) ~ height, Eq height, C horiz, C vert, C nrhs) => Array (Triangular lo diag up shape) a -> Full vert horiz height nrhs a -> Full vert horiz height nrhs a Source #
(Content lo, Content up, TriDiag diag, C size) => FormatArray (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Format Methods formatArray :: Floating a => String -> Array (Triangular lo diag up size) a -> Box Source #
(C sizeA, sizeA ~ sizeB, Eq sizeB, MultiplyTriangular loA upA loB upB, TriDiag diagA, TriDiag diagB) => Multiply (Triangular loA diagA upA sizeA) (Triangular loB diagB upB sizeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Triangular loA diagA upA sizeA) (Triangular loB diagB upB sizeB) :: Type Methods (<#>) :: Floating a => Array (Triangular loA diagA upA sizeA) a -> Array (Triangular loB diagB upB sizeB) a -> Array (Multiplied (Triangular loA diagA upA sizeA) (Triangular loB diagB upB sizeB)) a Source #
(Content lo, Content up, TriDiag diag, C vert, C horiz, C size, size ~ height, Eq height, C width) => Multiply (Triangular lo diag up size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Triangular lo diag up size) (Full vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (Triangular lo diag up size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (Triangular lo diag up size) (Full vert horiz height width)) a Source #
(Content lo, Content up, TriDiag diag, C vert, C horiz, C size, size ~ width, Eq width, C height) => Multiply (Full vert horiz height width) (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vert horiz height width) (Triangular lo diag up size) :: Type Methods (<#>) :: Floating a => Array (Full vert horiz height width) a -> Array (Triangular lo diag up size) a -> Array (Multiplied (Full vert horiz height width) (Triangular lo diag up size)) a Source #
type Index (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type Index (Triangular lo diag up size) = (Index size, Index size)
type HeightOf (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Triangular lo diag up size) = size
type WidthOf (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Triangular lo diag up size) = size

type Identity = Triangular Empty Unit Empty Source #

type Diagonal = Triangular Empty NonUnit Empty Source #

type LowerTriangular diag = Triangular Filled diag Empty Source #

type UpperTriangular diag = Triangular Empty diag Filled Source #

type Symmetric = FlexSymmetric NonUnit Source #

diagonal :: Order -> size -> Triangular Empty NonUnit Empty size Source #

lowerTriangular :: Order -> size -> LowerTriangular NonUnit size Source #

upperTriangular :: Order -> size -> UpperTriangular NonUnit size Source #

symmetric :: Order -> size -> Symmetric size Source #

autoDiag :: TriDiag diag => diag Source #

autoUplo :: (Content lo, Content up) => (lo, up) Source #

type DiagUpLo lo up = (DiagUpLoC lo up, DiagUpLoC up lo) Source #

switchDiagUpLoSym :: (Content lo, Content up) => f Empty Empty -> f Empty Filled -> f Filled Empty -> f Filled Filled -> f lo up Source #

class TriDiag diag Source #

Minimal complete definition

switchTriDiag

Instances

TriDiag NonUnit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods switchTriDiag :: f Unit -> f NonUnit -> f NonUnit Source #
TriDiag Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods switchTriDiag :: f Unit -> f NonUnit -> f Unit Source #

switchTriDiag :: TriDiag diag => f Unit -> f NonUnit -> f diag Source #

data Unit Source #

Constructors

Unit

Instances

Eq Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Unit -> Unit -> Bool # (/=) :: Unit -> Unit -> Bool #
Show Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Unit -> ShowS # show :: Unit -> String # showList :: [Unit] -> ShowS #
TriDiag Unit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods switchTriDiag :: f Unit -> f NonUnit -> f Unit Source #

data NonUnit Source #

Constructors

NonUnit

Instances

Eq NonUnit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: NonUnit -> NonUnit -> Bool # (/=) :: NonUnit -> NonUnit -> Bool #
Show NonUnit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> NonUnit -> ShowS # show :: NonUnit -> String # showList :: [NonUnit] -> ShowS #
TriDiag NonUnit Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods switchTriDiag :: f Unit -> f NonUnit -> f NonUnit Source #

data Banded sub super vert horiz height width Source #

Constructors

Banded
Fields bandedOffDiagonals :: (UnaryProxy sub, UnaryProxy super) bandedOrder :: Order bandedExtent :: Extent vert horiz height width

Instances

(Natural offDiag, Natural sub, Natural super, C vert, C horiz, C size, size ~ height, Eq height, C width, Eq width) => Multiply (BandedHermitian offDiag size) (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (BandedHermitian offDiag size) a -> Array (Banded sub super vert horiz height width) a -> Array (Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width)) a Source #
(Natural sub, Natural super, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB) :: Type Methods (<#>) :: Floating a => Array (Full vertA horizA heightA widthA) a -> Array (Banded sub super vertB horizB heightB widthB) a -> Array (Multiplied (Full vertA horizA heightA widthA) (Banded sub super vertB horizB heightB widthB)) a Source #
(C vert, C horiz, Eq height, Eq width) => Eq (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: Banded sub super vert horiz height width -> Banded sub super vert horiz height width -> Bool # (/=) :: Banded sub super vert horiz height width -> Banded sub super vert horiz height width -> Bool #
(Natural sub, Natural super, C vert, C horiz, Show height, Show width) => Show (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> Banded sub super vert horiz height width -> ShowS # show :: Banded sub super vert horiz height width -> String # showList :: [Banded sub super vert horiz height width] -> ShowS #
(Natural sub, Natural super, C vert, C horiz, C height, C width) => C (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods size :: Banded sub super vert horiz height width -> Int # uncheckedSize :: Banded sub super vert horiz height width -> Int #
(Natural sub, Natural super, C vert, C horiz, Indexed height, Indexed width) => Indexed (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type Index (Banded sub super vert horiz height width) :: Type # Methods indices :: Banded sub super vert horiz height width -> [Index (Banded sub super vert horiz height width)] # offset :: Banded sub super vert horiz height width -> Index (Banded sub super vert horiz height width) -> Int # uncheckedOffset :: Banded sub super vert horiz height width -> Index (Banded sub super vert horiz height width) -> Int # inBounds :: Banded sub super vert horiz height width -> Index (Banded sub super vert horiz height width) -> Bool # sizeOffset :: Banded sub super vert horiz height width -> (Int, Index (Banded sub super vert horiz height width) -> Int) # uncheckedSizeOffset :: Banded sub super vert horiz height width -> (Int, Index (Banded sub super vert horiz height width) -> Int) #
(Natural sub, Natural super, C vert, C horiz, InvIndexed height, InvIndexed width) => InvIndexed (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods indexFromOffset :: Banded sub super vert horiz height width -> Int -> Index (Banded sub super vert horiz height width) # uncheckedIndexFromOffset :: Banded sub super vert horiz height width -> Int -> Index (Banded sub super vert horiz height width) #
(Natural sub, Natural super, C vert, C horiz, NFData height, NFData width) => NFData (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: Banded sub super vert horiz height width -> () #
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Box (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Banded sub super vert horiz height width) :: Type Source # type WidthOf (Banded sub super vert horiz height width) :: Type Source # Methods height :: Banded sub super vert horiz height width -> HeightOf (Banded sub super vert horiz height width) Source # width :: Banded sub super vert horiz height width -> WidthOf (Banded sub super vert horiz height width) Source #
(Natural sub, Natural super, C vert, C horiz, Indexed height, Indexed width) => Indexed (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Indexed Methods (#!) :: Floating a => Array (Banded sub super vert horiz height width) a -> (Index (HeightOf (Banded sub super vert horiz height width)), Index (WidthOf (Banded sub super vert horiz height width))) -> a Source #
(Natural sub, Natural super, C vert, C horiz, Eq height, C width, C height) => MultiplyLeft (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (<#) :: Floating a => Vector (HeightOf (Banded sub super vert horiz height width)) a -> Array (Banded sub super vert horiz height width) a -> Vector (WidthOf (Banded sub super vert horiz height width)) a Source #
(Natural sub, Natural super, C vert, C horiz, Eq width, C width, C height) => MultiplyRight (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (#>) :: Floating a => Array (Banded sub super vert horiz height width) a -> Vector (WidthOf (Banded sub super vert horiz height width)) a -> Vector (HeightOf (Banded sub super vert horiz height width)) a Source #
(Natural sub, Natural super, vert ~ Small, horiz ~ Small, C width, C height, width ~ height) => Solve (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods solve :: (Floating a, HeightOf (Banded sub super vert horiz height width) ~ height0, Eq height0, C horiz0, C vert0, C nrhs) => Array (Banded sub super vert horiz height width) a -> Full vert0 horiz0 height0 nrhs a -> Full vert0 horiz0 height0 nrhs a Source #
(Natural sub, Natural super, C vert, C horiz, C height, C width) => FormatArray (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Format Methods formatArray :: Floating a => String -> Array (Banded sub super vert horiz height width) a -> Box Source #
(Natural offDiag, Natural sub, Natural super, C vert, C horiz, C size, size ~ width, Eq width, C height, Eq height) => Multiply (Banded sub super vert horiz height width) (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size) :: Type Methods (<#>) :: Floating a => Array (Banded sub super vert horiz height width) a -> Array (BandedHermitian offDiag size) a -> Array (Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size)) a Source #
(Natural sub, Natural super, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB) :: Type Methods (<#>) :: Floating a => Array (Banded sub super vertA horizA heightA widthA) a -> Array (Full vertB horizB heightB widthB) a -> Array (Multiplied (Banded sub super vertA horizA heightA widthA) (Full vertB horizB heightB widthB)) a Source #
(Natural subA, Natural superA, Natural subB, Natural superB, C vertA, C horizA, C vertB, C horizB, C heightA, C widthA, C widthB, widthA ~ heightB, Eq heightB) => Multiply (Banded subA superA vertA horizA heightA widthA) (Banded subB superB vertB horizB heightB widthB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Banded subA superA vertA horizA heightA widthA) (Banded subB superB vertB horizB heightB widthB) :: Type Methods (<#>) :: Floating a => Array (Banded subA superA vertA horizA heightA widthA) a -> Array (Banded subB superB vertB horizB heightB widthB) a -> Array (Multiplied (Banded subA superA vertA horizA heightA widthA) (Banded subB superB vertB horizB heightB widthB)) a Source #
type Index (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type Index (Banded sub super vert horiz height width) = BandedIndex (Index height) (Index width)
type HeightOf (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Banded sub super vert horiz height width) = height
type WidthOf (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Banded sub super vert horiz height width) = width

type BandedGeneral sub super = Banded sub super Big Big Source #

type BandedSquare sub super size = Banded sub super Small Small size size Source #

type BandedLowerTriangular sub size = BandedSquare sub U0 size Source #

type BandedUpperTriangular super size = BandedSquare U0 super size Source #

type BandedDiagonal size = BandedSquare U0 U0 size Source #

data BandedIndex row column Source #

Constructors

InsideBox row column
VertOutsideBox Int column
HorizOutsideBox row Int

Instances

(Eq row, Eq column) => Eq (BandedIndex row column) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: BandedIndex row column -> BandedIndex row column -> Bool # (/=) :: BandedIndex row column -> BandedIndex row column -> Bool #
(Show row, Show column) => Show (BandedIndex row column) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> BandedIndex row column -> ShowS # show :: BandedIndex row column -> String # showList :: [BandedIndex row column] -> ShowS #

bandedGeneral :: (UnaryProxy sub, UnaryProxy super) -> Order -> height -> width -> Banded sub super Big Big height width Source #

bandedSquare :: (UnaryProxy sub, UnaryProxy super) -> Order -> size -> Banded sub super Small Small size size Source #

bandedFromFull :: (UnaryProxy sub, UnaryProxy super) -> Full vert horiz height width -> Banded sub super vert horiz height width Source #

type UnaryProxy a = Proxy (Un a) Source #

addOffDiagonals :: (Natural subA, Natural superA, Natural subB, Natural superB, (subA :+: subB) ~ subC, (superA :+: superB) ~ superC) => (UnaryProxy subA, UnaryProxy superA) -> (UnaryProxy subB, UnaryProxy superB) -> ((Nat subC, Nat superC), (UnaryProxy subC, UnaryProxy superC)) Source #

class Content c Source #

Minimal complete definition

switchContent

data BandedHermitian off size Source #

Constructors

BandedHermitian
Fields bandedHermitianOffDiagonals :: UnaryProxy off bandedHermitianOrder :: Order bandedHermitianSize :: size

Instances

Eq size => Eq (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods (==) :: BandedHermitian off size -> BandedHermitian off size -> Bool # (/=) :: BandedHermitian off size -> BandedHermitian off size -> Bool #
(Natural off, Show size) => Show (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods showsPrec :: Int -> BandedHermitian off size -> ShowS # show :: BandedHermitian off size -> String # showList :: [BandedHermitian off size] -> ShowS #
(Natural off, C size) => C (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods size :: BandedHermitian off size -> Int # uncheckedSize :: BandedHermitian off size -> Int #
(Natural off, Indexed size) => Indexed (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type Index (BandedHermitian off size) :: Type # Methods indices :: BandedHermitian off size -> [Index (BandedHermitian off size)] # offset :: BandedHermitian off size -> Index (BandedHermitian off size) -> Int # uncheckedOffset :: BandedHermitian off size -> Index (BandedHermitian off size) -> Int # inBounds :: BandedHermitian off size -> Index (BandedHermitian off size) -> Bool # sizeOffset :: BandedHermitian off size -> (Int, Index (BandedHermitian off size) -> Int) # uncheckedSizeOffset :: BandedHermitian off size -> (Int, Index (BandedHermitian off size) -> Int) #
(Natural off, InvIndexed size) => InvIndexed (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods indexFromOffset :: BandedHermitian off size -> Int -> Index (BandedHermitian off size) # uncheckedIndexFromOffset :: BandedHermitian off size -> Int -> Index (BandedHermitian off size) #
(Natural off, NFData size) => NFData (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Methods rnf :: BandedHermitian off size -> () #
(Natural off, C size) => Box (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (BandedHermitian off size) :: Type Source # type WidthOf (BandedHermitian off size) :: Type Source # Methods height :: BandedHermitian off size -> HeightOf (BandedHermitian off size) Source # width :: BandedHermitian off size -> WidthOf (BandedHermitian off size) Source #
(Natural off, Indexed size) => Indexed (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Indexed Methods (#!) :: Floating a => Array (BandedHermitian off size) a -> (Index (HeightOf (BandedHermitian off size)), Index (WidthOf (BandedHermitian off size))) -> a Source #
(Natural offDiag, C size, Eq size) => MultiplyLeft (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (<#) :: Floating a => Vector (HeightOf (BandedHermitian offDiag size)) a -> Array (BandedHermitian offDiag size) a -> Vector (WidthOf (BandedHermitian offDiag size)) a Source #
(Natural offDiag, C size, Eq size) => MultiplyRight (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Methods (#>) :: Floating a => Array (BandedHermitian offDiag size) a -> Vector (WidthOf (BandedHermitian offDiag size)) a -> Vector (HeightOf (BandedHermitian offDiag size)) a Source #
(Natural offDiag, C size) => Solve (BandedHermitian offDiag size) Source #	There is no solver for indefinite matrices. Thus the instance will fail for indefinite but solvable systems.
Instance details Defined in Numeric.LAPACK.Matrix.Divide Methods solve :: (Floating a, HeightOf (BandedHermitian offDiag size) ~ height, Eq height, C horiz, C vert, C nrhs) => Array (BandedHermitian offDiag size) a -> Full vert horiz height nrhs a -> Full vert horiz height nrhs a Source #
(Natural offDiag, C size) => FormatArray (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Format Methods formatArray :: Floating a => String -> Array (BandedHermitian offDiag size) a -> Box Source #
(Natural offDiagA, Natural offDiagB, C sizeA, sizeA ~ sizeB, C sizeB, Eq sizeB) => Multiply (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB) :: Type Methods (<#>) :: Floating a => Array (BandedHermitian offDiagA sizeA) a -> Array (BandedHermitian offDiagB sizeB) a -> Array (Multiplied (BandedHermitian offDiagA sizeA) (BandedHermitian offDiagB sizeB)) a Source #
(Natural offDiag, C vert, C horiz, C size, size ~ height, Eq height, C width, Eq width) => Multiply (BandedHermitian offDiag size) (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (BandedHermitian offDiag size) (Full vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (BandedHermitian offDiag size) a -> Array (Full vert horiz height width) a -> Array (Multiplied (BandedHermitian offDiag size) (Full vert horiz height width)) a Source #
(Natural offDiag, Natural sub, Natural super, C vert, C horiz, C size, size ~ height, Eq height, C width, Eq width) => Multiply (BandedHermitian offDiag size) (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width) :: Type Methods (<#>) :: Floating a => Array (BandedHermitian offDiag size) a -> Array (Banded sub super vert horiz height width) a -> Array (Multiplied (BandedHermitian offDiag size) (Banded sub super vert horiz height width)) a Source #
(Natural offDiag, C vert, C horiz, C size, size ~ width, Eq width, C height, Eq height) => Multiply (Full vert horiz height width) (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Full vert horiz height width) (BandedHermitian offDiag size) :: Type Methods (<#>) :: Floating a => Array (Full vert horiz height width) a -> Array (BandedHermitian offDiag size) a -> Array (Multiplied (Full vert horiz height width) (BandedHermitian offDiag size)) a Source #
(Natural offDiag, Natural sub, Natural super, C vert, C horiz, C size, size ~ width, Eq width, C height, Eq height) => Multiply (Banded sub super vert horiz height width) (BandedHermitian offDiag size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Multiply Associated Types type Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size) :: Type Methods (<#>) :: Floating a => Array (Banded sub super vert horiz height width) a -> Array (BandedHermitian offDiag size) a -> Array (Multiplied (Banded sub super vert horiz height width) (BandedHermitian offDiag size)) a Source #
type Index (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type Index (BandedHermitian off size) = BandedIndex (Index size) (Index size)
type HeightOf (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (BandedHermitian off size) = size
type WidthOf (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (BandedHermitian off size) = size

bandedHermitian :: UnaryProxy off -> Order -> size -> BandedHermitian off size Source #

class C shape => Box shape Source #

Minimal complete definition

height, width

Instances

C size => Box (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Hermitian size) :: Type Source # type WidthOf (Hermitian size) :: Type Source # Methods height :: Hermitian size -> HeightOf (Hermitian size) Source # width :: Hermitian size -> WidthOf (Hermitian size) Source #
(Natural off, C size) => Box (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (BandedHermitian off size) :: Type Source # type WidthOf (BandedHermitian off size) :: Type Source # Methods height :: BandedHermitian off size -> HeightOf (BandedHermitian off size) Source # width :: BandedHermitian off size -> WidthOf (BandedHermitian off size) Source #
(Content lo, TriDiag diag, Content up, C size) => Box (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Triangular lo diag up size) :: Type Source # type WidthOf (Triangular lo diag up size) :: Type Source # Methods height :: Triangular lo diag up size -> HeightOf (Triangular lo diag up size) Source # width :: Triangular lo diag up size -> WidthOf (Triangular lo diag up size) Source #
(C vert, C horiz, C height, C width) => Box (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Full vert horiz height width) :: Type Source # type WidthOf (Full vert horiz height width) :: Type Source # Methods height :: Full vert horiz height width -> HeightOf (Full vert horiz height width) Source # width :: Full vert horiz height width -> WidthOf (Full vert horiz height width) Source #
(Eq lower, C vert, C horiz, C height, C width) => Box (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Split lower vert horiz height width) :: Type Source # type WidthOf (Split lower vert horiz height width) :: Type Source # Methods height :: Split lower vert horiz height width -> HeightOf (Split lower vert horiz height width) Source # width :: Split lower vert horiz height width -> WidthOf (Split lower vert horiz height width) Source #
(Natural sub, Natural super, C vert, C horiz, C height, C width) => Box (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private Associated Types type HeightOf (Banded sub super vert horiz height width) :: Type Source # type WidthOf (Banded sub super vert horiz height width) :: Type Source # Methods height :: Banded sub super vert horiz height width -> HeightOf (Banded sub super vert horiz height width) Source # width :: Banded sub super vert horiz height width -> WidthOf (Banded sub super vert horiz height width) Source #

type family HeightOf shape Source #

Instances

type HeightOf (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Hermitian size) = size
type HeightOf (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (BandedHermitian off size) = size
type HeightOf (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Triangular lo diag up size) = size
type HeightOf (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Full vert horiz height width) = height
type HeightOf (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Split lower vert horiz height width) = height
type HeightOf (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type HeightOf (Banded sub super vert horiz height width) = height

type family WidthOf shape Source #

Instances

type WidthOf (Hermitian size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Hermitian size) = size
type WidthOf (BandedHermitian off size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (BandedHermitian off size) = size
type WidthOf (Triangular lo diag up size) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Triangular lo diag up size) = size
type WidthOf (Full vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Full vert horiz height width) = width
type WidthOf (Split lower vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Split lower vert horiz height width) = width
type WidthOf (Banded sub super vert horiz height width) Source #
Instance details Defined in Numeric.LAPACK.Matrix.Shape.Private type WidthOf (Banded sub super vert horiz height width) = width

height :: Box shape => shape -> HeightOf shape Source #

width :: Box shape => shape -> WidthOf shape Source #